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x^{2} + 15 x + 50 = 0 (rearrange by adding 50 to both sides)
(x + 10)(x + 5) = 0 (factorise the quadratic equation)
x + 10 = 0 or x + 5 = 0 (for the above to equal zero, at least one of the bracketed terms must equal zero)
x = -10 or x = -5 (solving the two equations that result from step 3)
The solution is x = -10, x = -5